Question

In a random sample of 678 adult males 20 to 34 years of age, it was determined that 58 of them have hypertension(high blood pressure). a) what conditions must be checked in order to calculate a 96% confidence interval? b) Construct a 96% confidence for the proportion of adult males 20 to 34 years of age who have hypertension. Round the endpoints to 3 decimal places. c) If we wish to conduct our own study to determine the proportion of males 20 to 34 years of age who have hypertension, what sample size would be needed for the estimate to be within 3 percentage points with 96% confidence if you don't have a prior estimate?

Answer 1

a)
The data must be sampled randomly.

The sample values must be independent of each other.

When the sample is drawn without replacement (usually the case), the sample size, n, should be no more than 10% of the population.

The sample size must be sufficiently large.

b)

z value at 96% = 2.0537

phat = 58/678 = 0.086

CI = phat +/- z *sqrt(phat *(1-phat)/n)
= 0.086 +/- 2.0537 *sqrt*(0.086 *(1-0.086)/678)
= (0.063,0.108)

c)

ME = 0.03

ME = z * *sqrt(phat *(1-phat)/n)
0.03 = 2.0537 * sqrt*(0.086 *(1-0.086)/n)
n = (2.0537/0.03)^2 * (0.086*(1-0.086)
n = 17